Question

# The number which is neither prime nor composite is:(a) 0(b) 1(c) 2(d) 5

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Hint: We know that a number is a prime number when it has two positive divisors i.e. 1 and itself and a number is a composite number when it has more than two positive divisors and at least one of the divisors is not 1 and itself. Now, check the options given in the question which are neither prime nor composite.

We are asked to find the option which is neither prime nor composite. We know that a prime number is a number which has only two positive divisors i.e. 1 and itself.
A composite number is a number which has at least one its divisors not 1 or the number itself,
Now, we are going to check the options given in the above problem whether they are neither prime nor composite.
Checking option (a) 0 we get,
0 is not a prime number because there are infinite factors which we multiply by 0 gives 0 so the definition of prime number which has only two factors 1 and itself is not satisfying.
0 is not a composite number because it is not a positive integer which is not satisfying the fundamental arithmetic and 0 cannot be divided by itself then we will get $\dfrac{0}{0}$ which is an indeterminate form.
Hence, 0 is neither prime nor composite.
Hence, option (a) is correct.
Checking option (b) 1 we get,
1 is not a prime number because for a prime number the number should have two divisors 1 and itself. Now, 1 has only one divisor i.e. 1.
1 is not a composite number because a number to a composite number when it has a divisor which is not 1 and itself so here 1 has only one divisor i.e. 1.
Hence, 1 is neither a prime nor a composite number.
Hence, option (b) is correct.
Checking option (c) 2 we get,
2 is a prime number because it has two positive divisors 1 and 2 which is satisfying the definition of a prime number.
2 is not a composite number because it has not divisors which are other than 1 or itself.
Hence, 2 is a prime number but not a composite number.
Checking option (d) 5 we get,
5 is a prime number because it has two positive divisors 1 and 5 which is satisfying the definition of a prime number.
5 is not a composite number because it has not divisors which are other than 1 or itself.
Hence, 5 is a prime number but not a composite number.
From the above options, the correct option is (a) and (b).

Note: You might think 0 is a composite number because it has an infinite number of factors which on multiplication by 0 will give 0 but here 0 cannot be divisible by itself that’s why 0 is not a composite number.
You also might think that 1 is a prime number as if we multiply 1 by itself we get 1. But as you can see that the divisor 1 is creating ambiguity here like whether 1 is the number itself or the number 1 so 1 is not a prime number.